List of top Mathematics Questions asked in CUET (PG)

If \(f(z)=\frac{1}{z^2-3z+2}\)is expanded in the region |z|<1, then

The given series \(\frac{x}{1.3}+\frac{x^2}{2.4}+\frac{x^3}{3.5}+......,(x\gt0)\)is convergent in the interval

The volume generated by the revolution of the cardiod r = a(1-cosθ) about x-axis is

The function f(z) defined by \(f(z)= \begin{cases}     \frac{Re(z)}{z}       & z\neq0\\     0  & z=0   \end{cases}\)then which one of the following is true?

The value of \(\int\limits_C \frac{\sin\pi z^2+\cos\pi z^2}{(z-1)(z-2)}dz\), where C is the circle |z|=3 is

Which one of the following is not correct?

The integrating factor of the differential equation \(\frac{dy}{dx}=\frac{x^3+y^3}{xy^2}\)is

The order of the permutation\(\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\   2 & 4 & 6 & 5 & 1 & 3 \end{pmatrix}\)is

If λ₁,λ₂,λ₃ are the given values of the matrix \(\begin{bmatrix}   -2 & 2 & -3 \\   2 & 1 & -6 \\ -1 & -2 & 0 \end{bmatrix}\), then λ₁²+λ₂²+λ₃² is equal to

Let f(z) = u + iv be an analytic function, where u = x³-3xy² +3x² -3y², then the imaginary part v of f(z) is

Let f: R→R such that f(1) =3 and f'(1) = 6. Then \(\lim\limits_{x\rightarrow0}\left(\frac{f(1+x)}{f(1)}\right)^{1/x}\)equals

If f is twice differentiable function such that f''(x) = - f(x) and f'(x) = g(x), h(x) = [f(x)]²+[g(x)]² and h(5)=11, then h(10) =

If f(x) satisfies the conditions of Rolle's theorem in [1, 2] and f(x) is continuous in [1, 2], then \(\int_1^2f'(x)dx\) is equal to

Which one of the following statements is wrong.

Which one of the following is wrong?

The solution x₁ = 1, x₂ = 1, x₃ = 0 and z = 3 to the system of equations
x₁+x₂+x₃=2
x₁+x₂-x₃=2
x₁,x₂,x₃≥0
which minimizes z = x₁ + 2x₂ + 3x₃ is

If the matrices \(\left(\begin{matrix} 1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   -1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   i & 0 \\   0 & 0  \end{matrix}\right) and \left(\begin{matrix}   -i & 0 \\   0 & 0  \end{matrix}\right)\) form a group with respect to matrix multiplication, then which one of the following statements about the groups, thus formed is correct?

The solution of (x² -√2y) dx + (y² - √2x) dy = 0 is given by

Which of the following are generators of the multiplicative group {(1,2,3,4,5,6), x₇} where x₇ denotes multiplication moduls 7?

The matrix P is the inverse of a matrix Q. If I denotes the identity matrix, which one of the following options is correct?

In the neighborhood of z = 1, the function f(z) has a power series expansion of the form f(z) = 1+(1-z)+(1-z)² + .... then f(z) is

A rectangular box open at the top is to have volume of 32 cubic feets. The minimum outer surface area of the box is

The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4 × 4 symmetric positive definite matrix is

If income of A is 20% more than that of B, then income of B is how much percent less than that of A?

In a class of 49 students, the ratio of girls to boys is 4:3. If 4 girls leave the class, the ratio of girls to boys would be